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Science

Phase and Phase Difference (14-7) Learning Object

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- The angular argument of a harmonic wave’s function (whether it’s in sine or cosine) is its PHASE Ex. Measured in RADIANS, and its unit is phi (ϕ) Phase of a general harmonic wave function: Highlighted part = phase! *equations are from the textbook: (Equation 14-16) and (Equation 14-21)
- The difference between the phases (of a harmonic wave’s function) at two different points is the PHASE DIFFERENCE Its unit is Δϕ Equation for harmonic waves (where x2 and x1 (denoted as Δx) are different points on the same wave): *k = 2π/λ *equation is from the textbook: (Equation 14-22)
- You have 2 points at x1 and x2. If they are an integer multiple of wavelengths apart (ex. 1, 2, 3…), the points are IN PHASE The distance between the crests are either 1 or 2 (integers) wavelengths apart, as shown by the highlighted lengths. These points constantly have EQUAL displacements. Phase Difference = even multiple of π radians (ex. 2π or 4π) *image is from the textbook: (Figure 14-25)
- You have 2 points, A and B. If these points are an odd-half integer multiple of a wavelength apart (ex. 1/2, 3/2, 5/2…), they are OUT OF PHASE From : http://www.antonine-education.co.uk/Salters/MUS/images/Making5.gif Wavelength = 25 units. The distance between A and B are 12.5 (λ/2) units apart. They are π radians out of phase. These points constantly have EQUAL but OPPOSITE displacements from equilibrium.
- Two points on a wave on a string are 15m apart. The wave has a wavelength of 20m. What is the phase difference between the two points?
- Using Equation 14-22… λ = 20m, Δx = 15m, Δϕ = ? Δϕ = 2π(15/20) = 2π(3/4) = 3π/2 radians.